(1) Field of Invention
The invention relates to signal processing approaches for tracking systems and, more particularly, to a method for resolving harmonic ambiguity and inter array harmonic tracking that calculates a complete set of possible harmonic families given the automatic or manual selection of a target frequency from a frequency spectrum.
(2) Background of the Invention
Tracking systems utilize radiating beam-forming sources to probe an area to be searched so as to detect objects. For example, in conventional sonar devices a highly directional beam of sonic energy periodically radiates from a scanning transducer, and a receiver detects echoes reflected from object(s) within range. Modern active sonar systems commonly provide multibeam capabilities as well.
A detectable target typically return-radiates signals over a wide bandwidth. However, only energy from a single frequency is used for target detection in conventional passive sonar systems. Since only a fractional part of the total energy is present at any given frequency, this places a significant constraint on detection ability of conventional circuitry. When uncorrelated noise and clutter is added to the radiated signals, it becomes more and more difficult to identify target signals amidst the noisy signals. Thus, in a high noise environment, the resulting low signal to noise ratio of the target signature results in a generally unacceptable trade-off between no detection or unacceptable false alarms. The target signature will comprise a “fundamental” frequency together with an infinite number of harmonics, the amplitude of the Nth harmonic being 1/N of the amplitude of the fundamental component. The target signature is embedded in a noisy signal. The trick then is to resolve the target signature from amidst the noise despite ambiguity. Prior efforts have been undertaken to pursue this goal.
For example, U.S. Pat. No. 5,034,931 to Wells discloses a method for enhancing target detection through the processing of the fundamental frequency and a plurality of harmonics that are embedded in background noise. Signals comprising a fundamental frequency signal (fo) and a plurality of harmonic frequency signals (2fo, 3fo . . . nfo) embedded in the background noise are received for processing. The plurality of harmonic frequencies are processed to determine the background noise level and to determine which of the harmonic frequency signals contain harmonics of the fundamental frequency signal. The fundamental frequency signal and those harmonic signals that are harmonics thereof are integrated to provide a summed signal. The summed signal is then processed by comparing it to a threshold level that is a function of the background noise level to provide an enhanced target detection signal. The enhanced target detection signal is then displayed on a monitor.
In addition to the Wells '931 threshold approach, other types of signal processing include broad-band amplification, narrow band filtering, variable gain, automatic gain control (AGC), use of an adaptive filter for noise cancellation, neural net identification, FFT or wavelet-based analysis or decomposition, joint time frequency analysis, transfer functioning correlation techniques, template matching, beam-forming algorithms, timing measurements, harmonic analysis, use of decision trees, comparison with a data base and auto-calibration.
Unfortunately, the Wells '931 and other known automatic harmonic detection algorithms suffer from the ambiguity associated with the existence of multiple probable solutions. For example, a given harmonic set H=fo*[1 2 3 4 5 6 7 8 9 . . . ] will result in other possible sub-harmonic sets being selected such as J=fo*[2 4 6 8 . . . ] or K=fo*[3 6 9 12 15 . . . ], etc. These solutions are difficult to resolve in cases where the individual components vary in intensity from member to member. In the case where there is an intensity (power) distribution that coincides with even (or odd) harmonics the associated sub-harmonic set (i.e., J or K) can produce a more likely solution (i.e. total energy) than the set produced from the actual fundamental (i.e., H).
Another drawback to the traditional approaches is the existence of an infinite solution space, over which the search must be performed, thus requiring significant effort and/or computational overhead to resolve.
It would be greatly advantageous to provide a more practical and efficient method for resolving harmonic ambiguity and inter array harmonic tracking capable of calculating a complete set of possible harmonic families given the selection (by an operator) or automatic detection (by an automated algorithm) of a single tone (fselected) from a frequency spectrum using a novel “ambiguity matrix” approach in which a matrix of all N possible harmonic members and M hypothetical fundamentals is constructed. An ambiguity matrix would provide the operator with an image of all possible harmonic families associated with the selected tone. The selection of the correct fundamental could then be based on simple comparisons between this image of the set of all possible fundamentals. This ambiguity matrix would effectively provide a greatly-reduced and finite solution space (a discrete set of possibilities) in which to unambiguously estimate the correct fundamental.